In the short run,a competitive firm has a marginal product of labor,MPL = 2L^-0.25.The output price is $4 per unit and the wage is $5 per hour.The short-run labor demand curve for the firm is A) 10L^-0.25. B) 8L^-0.5. C) 4L^0.25. D) 8L^-0.25.

Question

Quizplus · Accepted Answer

To find the labor demand curve, we need to maximize the profit of the firm. Total revenue = output price x output quantity Total cost = wage x labor input Profit = Total revenue - Total cost Profit = 4Q - 5L We take the derivative of profit with respect to L to find the MRP (Marginal Revenue Product) of labor, which is the same as MPL (Marginal Product of Labor) in a competitive market: MRP = d(4Q - 5L)/dL = -5 MPL = 2L^-0.25 Setting MRP equal to the wage rate, we can solve for the labor demand curve: MRP = MPL x output price = wage -5 = (2L^-0.25) x 4 -5/8 = L^-0.25 L = 8L^-0.25 Therefore, the answer is D.

In the Short Run,a Competitive Firm Has a Marginal Product